In this paper, a lattice Boltzmann model for one-dimensional nonlinear Dirac equation is presented by using double complex-valued distribution functions and carefully selected equilibrium distribution functions. The effects of space and time resolutions and relaxation time on the accuracy and stability of the model are numerically investigated in detail. It is found that the model is of second-order accuracy in both space and time, and the order of accuracy is near 3.0 at lower grid resolution, which shows that the lattice Boltzmann method is an effective numerical scheme for the nonlinear Dirac equation.

The circumstances under which a system reaches thermal equilibrium, and how to derive this from basic dynamical laws, has been a major question from the very beginning of thermodynamics and statistical mechanics. Despite considerable progress, it remains an open problem. Motivated by this issue, we address the more general question of equilibration. We prove, with virtually full generality, that reaching equilibrium is a universal property of quantum systems: almost any subsystem in interaction with a large enough bath will reach an equilibrium state and remain close to it for almost all times. We also prove several general results about other aspects of thermalization besides equilibration, for example, that the equilibrium state does not depend on the detailed microstate of the bath.

We present a study of the electrophoresis of long DNA in a strong electric field through a hexagonal array of cylindrical microscale posts spaced such that the pore size is commensurate with equilibrium coil size of the DNA. Experimental mobility, dispersivity, and videomicroscopy data indicate that the DNA frequently collide with the posts, contradicting previous Brownian dynamics studies using a uniform electric field. We demonstrate via simulations that the frequent collisions, which are essential to separations in these devices, are due to the nonuniform electric field, highlighting the importance of accounting for electric-field gradients when modeling DNA transport in microfluidic devices.

Normal development of multicellular organisms requires cells to respond properly according to their positions. Positional information is often provided to cells as concentrations of diffusive chemicals called morphogens with spatial gradients. However, the spatial profiles of their concentrations include various kinds of noises, making positional information unreliable. In many developmental systems, multiple morphogen gradients are adopted to specify the spatial position along a single axis, presumably to achieve a sufficiently high precision of information on the location of each cell. In this paper, we ask how the precision of positional information depends on the number of morphogens. We derive a formula for the limit of precision when each cell adopts the maximum-likelihood estimation of the “true” position from noisy inputs. The precision increases with the number of morphogens and interestingly it also depends on the correlation of noises. The positional specification can be made more precisely if their gradients are of the opposite (same) direction when noises of the two morphogens are positively (negatively) correlated. The formula also tells us a minimum number of morphogens needed to achieve a given precision of positional information. We illustrate the theory by analyzing experimental data for the gradients of two diffusive chemicals, Bicoid and Caudal, in the early development of Drosophila embryo. The analysis suggests that combined information provided by the two chemicals is able to give accurate positional information in the middle part of the embryo, where the embryo segmentation occurs in later stages, much more than near both ends.

Thin liquid films with floating active protein machines are considered. Cyclic mechanical motions within the machines, representing microscopic swimmers, lead to molecular propulsion forces applied to the air-liquid interface. We show that when the rate of energy supply to the machines exceeds a threshold, the flat interface becomes linearly unstable. As a result of this instability, the regime of interface turbulence, characterized by irregular traveling waves and propagating machine clusters, is established. Numerical investigations of this nonlinear regime are performed. Conditions for the experimental observation of the instability are discussed.

We theoretically study chaos synchronization of two lasers which are delay coupled via an active or a passive relay. While the lasers are synchronized, their dynamics is identical to a single laser with delayed feedback for a passive relay and identical to two delay-coupled lasers for an active relay. Depending on the coupling parameters the system exhibits bubbling, i.e., noise-induced desynchronization, or on-off intermittency. We associate the desynchronization dynamics in the coherence collapse and low-frequency fluctuation regimes with the transverse instability of some of the compound cavity’s antimodes. Finally, we demonstrate how, by using an active relay, bubbling can be suppressed.

We study an effect of large-scale coherent structures on global properties of turbulent convection in laboratory experiments in air flow in a rectangular chamber with aspect ratios $A\approx 2$ and $A\approx 4$ (with the Rayleigh numbers varying in the range from $5\times {10}^6$ to ${10}^8$). The large-scale coherent structures comprise the one-cell and two-cell flow patterns. We found that a main contribution to the turbulence kinetic-energy production in turbulent convection with large-scale coherent structures is due to the nonuniform large-scale motions. Turbulence in large Rayleigh number convection with coherent structures is produced by shear rather than by buoyancy. We determined the scalings of global parameters (e.g., the production and dissipation of turbulent kinetic energy, the turbulent velocity and integral turbulent scale, the large-scale shear, etc.) of turbulent convection versus the temperature difference between the bottom and the top walls of the chamber. These scalings are in an agreement with our theoretical predictions. We demonstrated that the degree of inhomogeneity of the turbulent convection with large-scale coherent structures is small.

The identification of flow pattern is a basic and important issue in multiphase systems. Because of the complexity of phase interaction in gas-liquid two-phase flow, it is difficult to discern its flow pattern objectively. In this paper, we make a systematic study on the vertical upward gas-liquid two-phase flow using complex network. Three unique network construction methods are proposed to build three types of networks, i.e., flow pattern complex network (FPCN), fluid dynamic complex network (FDCN), and fluid structure complex network (FSCN). Through detecting the community structure of FPCN by the community-detection algorithm based on $K$-mean clustering, useful and interesting results are found which can be used for identifying five vertical upward gas-liquid two-phase flow patterns. To investigate the dynamic characteristics of gas-liquid two-phase flow, we construct 50 FDCNs under different flow conditions, and find that the power-law exponent and the network information entropy, which are sensitive to the flow pattern transition, can both characterize the nonlinear dynamics of gas-liquid two-phase flow. Furthermore, we construct FSCN and demonstrate how network statistic can be used to reveal the fluid structure of gas-liquid two-phase flow. In this paper, from a different perspective, we not only introduce complex network theory to the study of gas-liquid two-phase flow but also indicate that complex network may be a powerful tool for exploring nonlinear time series in practice.

A two-dimensional mass conserving lattice Boltzmann method (LBM) has been developed for multiphase (liquid and vapor) flows with solid particles suspended within the liquid and/or vapor phases. The main modification to previous single-phase particle suspension models is the addition of surface (adhesive) forces between the suspended particle and the surrounding fluid. The multiphase dynamics between fluid phases is simulated via the single-component multiphase model of Shan and Chen [Phys. Rev. E 47, 1815 (1993)]. The combined multiphase particle suspension model is first validated and then used to simulate the dynamics of a single-suspended particle on a planar liquid-vapor interface and the interaction between a single particle and a free-standing liquid drop. It is observed that the dynamics of suspended particles near free-standing liquid droplets is affected by spurious velocity currents although the liquid-vapor interface itself is a local energy minimum for particles. Finally, results are presented for capillary interactions between two suspended particles on a liquid-vapor interface subjected to different external forces and for spinodal decomposition of a liquid-vapor mixture in the presence of suspended particles. Qualitative agreements are reached when compared with results of suspended particles in a binary mixture based on multicomponent LBM models.

We introduce an extension of the simple on-off ratchet by including a second asymmetric sawtooth potential with half the periodicity and inverse asymmetry in the ratchet cycle. As a result of this additional potential, the Brownian particles exhibit reversal of the direction of their mean displacement when relevant parameters such as the on time of the potentials are varied. This direction reversal offers new opportunities for microfluidic particle separation in sieve devices. Based on the results of our extended ratchet model, we propose two designs. Compared to the classical microfluidic sieve, the proposed devices can be made of significantly smaller sizes without sacrificing the resolution of the separation process. In fact, one of our devices can be reduced to a single channel. We study our extended ratchet model by Brownian dynamics simulations and derive analytical and approximative expressions for the mean displacement using an extension of the method of discrete steps. We show that these expressions are valid in relevant regions of the parameter space and that they can be used to predict the occurrence of direction reversal.

The physical properties of granular materials have been extensively studied in recent years. So far, however, there exists no theoretical framework which can explain the observations in a unified manner beyond the phenomenological jamming diagram. This work focuses on the case of static granular matter, where we have constructed a statistical ensemble which mirrors equilibrium statistical mechanics. This ensemble, which is based on the conservation properties of the stress tensor, is distinct from the original Edwards ensemble and applies to packings of deformable grains. We combine it with a field theoretical analysis of the packings, where the field is the Airy stress function derived from the force and torque balance conditions. In this framework, Point J characterized by a diverging stiffness of the pressure fluctuations. Separately, we present a phenomenological mean-field theory of the jamming transition, which incorporates the mean contact number as a variable. We link both approaches in the context of the marginal rigidity picture proposed by Wyart and others.

Flow-induced aggregation of colloidal particles leads to aggregates with fairly high fractal dimension $\left(d_f\simeq 2.4–3.0\right)$ which are directly responsible for the observed rheological properties of sheared dispersions. We address the problem of the decrease in aggregate size with increasing hydrodynamic stress, as a consequence of breakup, by means of a fracture-mechanics model complemented by experiments in a multipass extensional (laminar) flow device. Evidence is shown that as long as the inner density decay with linear size within the aggregate (due to fractality) is not negligible (as for $d_f\simeq 2.4–2.8$), this imposes a substantial limitation to the hydrodynamic fragmentation process as compared with nonfractal aggregates (where the critical stress is practically size independent). This is due to the fact that breaking up a fractal object leads to denser fractals which better withstand stress. In turbulent flows, accounting for intermittency introduces just a small deviation with respect to the laminar case, while the model predictions are equally in good agreement with experiments from the literature. Our findings are summarized in a diagram for the breakup exponent (governing the size versus stress scaling) as a function of fractal dimension.

We present a study of smectic focal conic domains in films of various liquid-crystal compounds on a solid substrate. Focal conic domains are generated as a result of the antagonistic anchoring conditions of the film surfaces, random planar at the substrate interface and homeotropic at the air interface. The curved arrangement of the smectic layers in focal conic domains leads to a depression in the film/air interface above each domain. Using atomic force microscopy, we determine the temperature dependence of the depth of the depressions in different smectic phases and at different phase transitions. In most cases, our results are not in accordance with the assumption of strictly incompressible smectic layers, and we discuss the observed behavior with respect to the known results on the layer compressibility modulus $B$.

The results of extensive molecular simulations of adsorption and diffusion of water vapor in polyaniline, made conducting by doping it with HCl or HBr over a broad range of temperatures, are reported. The atomistic model of the polymers was generated using energy minimization, equilibrium molecular dynamics simulations, and two different force fields. The computed sorption isotherms are in excellent agreement with the experimental data. The computed activation energies for the diffusion of water molecules in the polymers also compare well with what has been reported in the literature. The results demonstrate the potential of conducting polyaniline for water harvesting from air.

Most theories of homogeneous nucleation are based on a Fokker-Planck-like description of the behavior of the mass of clusters. Here we will show that these approaches are incomplete for a large class of nucleating systems, as they assume the effective dynamics of the clusters to be Markovian, i.e., memoryless. We characterize these non-Markovian dynamics and show how this influences the dynamics of clusters during nucleation. Our results are validated by simulations of a three-dimensional Ising model with locally conserved magnetization.

Outline of the derivation and mathematical and physical interpretations are presented for a discrete dynamical system known as the “poor man’s Navier-Stokes equation.” Numerical studies demonstrate that velocity fields produced by this dynamical system are similar to those seen in laboratory experiments and in detailed simulations, and they lead to scaling for the turbulence kinetic energy spectrum in accord with Kolmogorov K41 theory.

We present a formal connection between Lagrangian and Eulerian velocity increment distributions which is applicable to a wide range of turbulent systems ranging from turbulence in incompressible fluids to magnetohydrodynamic turbulence. For the case of the inverse cascade regime of two-dimensional turbulence we numerically estimate the transition probabilities involved in this connection. In this context we are able to directly identify the processes leading to strongly non-Gaussian statistics for the Lagrangian velocity increments.

Models of the elastic, inelastic, and reactive collisions of energetic hydrogen ions, atoms, and molecules are developed for predicting ${\text{H}}_{\alpha }$ and ${\text{H}}_2$ near-uv emission, ${\text{H}}_{\alpha }$ Doppler profiles, and ion energy distributions for low-pressure, low-current discharges in ${\text{H}}_2$. The model is applied to spatially uniform electric field $E$ to gas density $N$ ratios of $350\text{Td}\le E/N\le 45\text{kTd}$ and $8\times {10}^{19}\le Nd\le 10\times {10}^{21}{\text{m}}^{-2}$, where $d$ is the electrode separation and $1\text{Td}={10}^{-21}\text{V}{\text{m}}^2$. Mean ion energies at the cathode are 5–1500 eV. Cross sections for ${\text{H}}^{+}$, $\text{H}_2{}^{+}$, $\text{H}_3{}^{+}$, H, ${\text{H}}_2$, and excited $\text{H}\left(n=3\right)$ collisions with ${\text{H}}_2$ and reflection probabilities from electrodes are updated and summarized. Spatial and energy distributions of ions and fast neutrals are calculated using a “multibeam” technique. At the lower $E/N$ and $Nd$, electron excitation of ${\text{H}}_{\alpha }$ dominates near the anode. Excitation of ${\text{H}}_{\alpha }$ by fast H atoms near the cathode increases rapidly with pressure through a multistep reaction sequence. At higher $E/N$, fast H atoms produced at the cathode surface excite much of the ${\text{H}}_{\alpha }$. The model agrees with experimental spatial distributions of ${\text{H}}_{\alpha }$ emission and Doppler profiles. Ion energy distributions agree with experiments only for $\text{H}_2{}^{+}$. Cross sections are derived for excitation of the near-uv continuum of ${\text{H}}_2$ by H atoms.

In this paper we propose a highly efficient and stable lattice Boltzmann method for solving low Reynolds number exterior flows using a preconditioning technique. The present method is based on replacing the constant preconditioning parameter $\left(\gamma \right)$ within uniform grids [Guo et al., Phys. Rev. E 70, 066706 (2004)] by a space- and time-dependent one in a nested mesh-refined domain. To do this, for the transition from a fine to the neighboring coarser grid, $\gamma$ has been divided by a factor $K$, which is large initially and anneals stepwise to a small value after some iterations. With this technique, more than one order of magnitude larger convergence rate can be achieved, and several orders of magnitude larger system size can be treated.

An isothermal model on the standard two-dimension nine-velocity lattice (D2Q9) is proposed and analyzed. It originates from the thermal model with energy conservation introduced by N. I. Prasianakis and I. V. Karlin [Phys. Rev. E 76, 016702 (2007)]. The isothermal and the thermal equivalent models are tested through the simulation of the decay of a shear wave and of a temperature wave. Both are shown to be Galilean invariant, reference temperature independent, and rotational isotropic through the measurement of the transport coefficients on a rotated moving frame of reference.